RoboguruRoboguru
SD

x→∞lim​(3x−4)(x−1)(x+5)(2x+3)​=…

Pertanyaan

limit as x rightwards arrow infinity of fraction numerator open parentheses x plus 5 close parentheses open parentheses 2 x plus 3 close parentheses over denominator open parentheses 3 x minus 4 close parentheses open parentheses x minus 1 close parentheses end fraction equals horizontal ellipsis 

  1. 1 third 

  2. 2 over 3 

  3. 4 over 9 

  4. 3 

  5. infinity 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Dengan menggunakan konsep perkalian bentuk aljabar suku dua, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator open parentheses x plus 5 close parentheses open parentheses 2 x plus 3 close parentheses over denominator open parentheses 3 x minus 4 close parentheses open parentheses x minus 1 close parentheses end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 3 x plus 10 x plus 15 over denominator 3 x squared minus 3 x minus 4 x plus 4 end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator 2 x squared plus 13 x plus 15 over denominator 3 x squared minus 7 x plus 4 end fraction end cell end table 

Ingat kembali aturan limit tak hingga berikut ini.

Misal m dan n adalah bilangan bulat positif dan size 12px lim with size 12px x size 12px rightwards arrow size 12px infinity below fraction numerator size 12px a size 12px x to the power of size 12px m size 12px plus size 12px b size 12px x to the power of size 12px m size 12px minus size 12px 1 end exponent size 12px plus size 12px. size 12px. size 12px. size 12px plus size 12px c over denominator size 12px p size 12px x to the power of size 12px n size 12px plus size 12px q size 12px x to the power of size 12px n size 12px minus size 12px 1 end exponent size 12px plus size 12px. size 12px. size 12px. size 12px plus size 12px r end fraction size 12px equals size 12px L size 12px space, maka berlaku:

  • Jika m greater than n, maka L equals infinity 
  • Jika m equals n, maka L equals a over p
  • Jika m less than n, maka L equals 0      

Dengan aturan limit tak hingga di atas maka diperoleh perhitungan sebagai berikut.

Pada table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x squared plus 13 x plus 15 over denominator 3 x squared minus 7 x plus 4 end fraction end cell end table diperoleh bahwa

  • m equals 2 
  • n equals 2 
  • a equals 2 
  • p equals 3 

Lalu, karena m equals n maka berlaku L equals a over p, sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x squared plus 13 x plus 15 over denominator 3 x squared minus 7 x plus 4 end fraction end cell end table equals 2 over 3 

Dengan demikian hasil limit as x rightwards arrow infinity of fraction numerator open parentheses x plus 5 close parentheses open parentheses 2 x plus 3 close parentheses over denominator open parentheses 3 x minus 4 close parentheses open parentheses x minus 1 close parentheses end fraction equals 2 over 3.

Jadi, jawaban yang tepat adalah B.

34

5.0 (1 rating)

Pertanyaan serupa

Nilai x→∞lim​ (7+3x)(2−x)(6+x)(3−7x)​= …

34

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia